दिक्कोज्या, दिक अनुपात | Three Dimensional Geometry | 12th Maths | Chap 13 | Lec 01 |By Akhilesh Sir

Class 12 Maths | Chapter 11 Three Dimensional Geometry | Important Questions and Quick Revision

Three Dimensional Geometry Part 1 - Most Important Questions + Quick Revision | JEE Mains 2020 Maths

Three Dimensional Geometry Part 2 - Most Important Questions + Quick Revision | JEE Mains 2020 Maths

If matrix A=[[1,2,3], [4,1,2], [1,-1,2]] B= [[2,1,3], [4,1,-1], [2,2,3]] C= [[14], [12], [2]] D= [[13], [11], [14]]. When X= [[x], [y],[z]] is such that solutions of equations AX=C and BX=D represents two points L and M in three dimensional space. If l' and M' are the reflection of points L and M in the plane x+y+z=9 then find values of L,M,L' and M'

The average of 24 numbers is 56. The average of the first 10 numbers is 71.7 and that of the next 11 numbers is 42. The next three numbers (i.e 22nd ,23rd and 24th) are in the ratio 1/2 : 1/3: 5/12 . What is the average of the 22nd and 24th numbers? 24 संख्याओं का औसत 56 है | पहली 10 संख्याओं का औसत 71.7 है तथा अगली 11 संख्याओं का औसत 42 है| अगली तीन संख्याएँ ( अर्थात 22वीं, 23वीं तथा 24वीं ) 1/2 : 1/3: 5/12 के अनुपात में हैं | 22वीं तथा 24वीं संख्याओं का औसत कितना है ?

The average of thirteen numbers is 47. The average of the first three numbers is 39 and that of the next seven numbers is 49. The 11th number is two times the 12th number and 12th number is 3 less than the 13th number. What is the average of 11th and 13th numbers? तेरह संख्याओं का औसत 47 है | पहली तीन संख्याओं का औसत 39 है तथा अगली सात संख्याओं का औसत 49 है | 11वीं संख्या 12वीं संख्या से दोगुनी है तथा 12वीं संख्या 13वीं संख्या से 3 कम है | 11वीं और 13वीं संख्याओं का औसत ज्ञात करें |

In a class, 18 students took Physics, 23 students took Chemistry and 24 students took Mathematics of these 13 took both Chemistry and Mathematics, 12 took both Physics and Chemistry and 11 took both Physics and Mathematics. If 6 students offered all the three subjects, find: (ii) How many took Maths but not Chemistry.

There are ten exams to be conducted from 9 to 13 of a month. There are two time slots for every day, morning slot and evening slot. The maximum marks of these exams are from 70 to 160. The maximum marks of every subject are unique. The time durations of the exams is from the range of 1hr to 5hr. The time duration is also unique for each subject. The subjects are Math, English, Physics, Bio, Chemistry, Economices, History, Home Science, Geography and Accounts. The first exam is of math and of 2hrs. The time duration of last exam is 15 minutes more than first exam. The exam of English is of 80 marks and on the same day of the exam of math. Total marks of the exams of first day are 180 marks. There are two exams between history and accounts. The last exam is of accounts and of 110 marks. There are three exams between English and the exam which is of 90 marks. The exam of physics is in morning and it is on an even date. The exam of 3hr and 5hr are on the same day. The sum of timings of math and physics is 5hr. The exam of 130 marks and 90 marks are on the same day. The exam of chemistry is not of 90 marks. The exam of geography is of 4^(1//2) hrs. and on the last day. The exam of home science is on an even date and of least marks. The exam of chemistry is before exam of economics. The exam of 150 marks is of maximum time duration. The exam of economics is of economics is of least time duration. The sum of time duration of economics and history is of 5hrs. The exam of Chemistry is of 3^(1//2) hrs. duration. The maximum marks of physics is 30 marks less than that of biology. The maximum marks of 4^(1//2) hrs. exam is 30 marks more than marks of accounts. History is of maximum marks. The maximum marks of home-science are least of all. Which two exams are scheduled for 10^(th) of the month?

The average of thirteen numbers is 47. The average of the first three numbers is 39 and that of next seven numbers is 49. The 11^(th) number is two times the 12^(th) number and 12^(th) number is 3 less that the 13^(th) number. What is the average of 11^(th) and 13^(th) numbers ?